- Email: [email protected]
Study of effective atomic number of breast tissues determined using the elastic to inelastic scattering ratio
Nuclear Instruments and Methods in Physics Research A 652 (2011) 739–743
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Study of effective atomic number of breast tissues determined using the elastic to inelastic scattering ratio M. Antoniassi, A.L.C. Conceic- a~ o, M.E. Poletti n ~ Preto, Universidade de Sa~ o Paulo, Ribeirao ~ Preto, Sa~ o Paulo, Brazil ´tica, Faculdade de Filosofia Ciˆencias e Letras de Ribeirao Departamento de Fı´sica e Matema
a r t i c l e in fo
abstract
Available online 1 October 2010
In this work we have measured Compton and Rayleigh scattering radiation from normal (adipose and fibroglandular), benign (fibroadenoma) and malignant (ductal carcinoma) breast tissues using a monoenergetic beam of 17.44 keV and a scattering angle of 901 (x ¼ 0.99 A˚ 1). A practical method using the area of Rayleigh and Compton scattering was used for determining the effective atomic number (Zeff) of the samples, being validated through measurements of several reference materials. The results show that there are differences in the distributions of Zeff of breast tissues, which are mainly related to the elemental composition of carbon (Z ¼6) and oxygen (Z¼ 8) of each tissue type. The results suggest that is possible to use the method to characterize the breast tissues permitting study histological features of the breast tissues related to their elemental composition. & 2010 Elsevier B.V. All rights reserved.
Keywords: Effective atomic number Elastic scattering Inelastic scattering Breast cancer
1. Introduction The scattered radiation both elastically (Rayleigh) and inelastically (Compton) has been widely reported as an important tool for characterization of materials [1–3]. Specifically for medical purposes, it has been successfully used to characterize biological tissues [4–6]. The elastic scattering allows obtaining the spatial distribution of the scattering centers (atoms or molecules) giving detailed information about the chemical structures of the tissues, being applied for different tissues like breast [7–11], brain [12], kidney [13], uterus [13] and muscle [14]. On the other hand, the inelastic (Compton) scattering allows assessing the electron density of the tissues [15], since its intensity depends upon the number of scattering centers (electrons) in sample volume, being applied successfully in bone [16,17], lung [18,19] and breast densitometry [20–22] for osteoporosis, lung oedema and breast cancer diagnoses, respectively. The combination of elastic and inelastic scattering through the ratio of their intensities, will give a quantity dependent only on a function of the atomic number [23], independent of the density and attenuation inside the sample, which allows determining the effective atomic number of the human tissues, an important quantity used in medical imaging (particularly in tomographic systems) and dosimetry [24]. When compared with conventional transmission techniques, sensitive to linear attenuation coefficient (m), this technique is especially useful in cases where variations
n
Corresponding author. Tel.: + 55 16 3602 4442; fax: + 55 16 3602 4887. E-mail address: [email protected] (M.E. Poletti).
0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.09.110
of m are small, and the atomic number variations become more significant. It has been used to detect changes in the composition of soft tissue [25], liver [26] and trabecular bone [27,28]. However, there are few works for breast tissue characterization [29]. For this purpose, Ryan and Farquharson [29] measured elastic and inelastic scattering of normal (healthy) and malignant breast tissues using a monoenergetic synchrotron beam of 10 keV and a scattering angle of 1201. Gelatine-based gel mixtures were used to calibrate the system in order to obtain the mean atomic number of the tissues from the elastic to inelastic scattering ratio. In the present work we have measured elastic and inelastic scattering radiation from normal (adipose and fibroglandular), benign (fibroadenoma) and malignant (carcinoma) breast tissues using a monoenergetic beam of 17.44 keV and a scattering angle of 901 (x ¼0.99 A˚ 1). A practical method using the area of elastic and inelastic scattering was used for determining the effective atomic number (Zeff) [23] of the breast tissues. This work also discusses the results on the basis of histological characteristics and elemental composition of the tissues. Finally, statistical comparisons were made in order to evaluate the potential use of effective atomic number to classify breast tissues.
2. Materials and method 2.1. Experimental arrangement The experimental set-up is shown in Fig. 1. The X-ray tube used was a Mo (Z¼42, Ka ¼17.44 keV, Kb ¼ 19.6 keV) coupled to a high voltage generator of 4 kV operating at 35 kVp and 45 mA.
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M. Antoniassi et al. / Nuclear Instruments and Methods in Physics Research A 652 (2011) 739–743
2.3. Method When a detector is placed in a determined angle relative to the incident direction of the radiation (scattering angle), usually two features are detected (considering a high energy resolution detection system): a narrow peak in the same energy of the incident radiation, corresponding to the photons elastically (Rayleigh) scattered and a wide peak with energy lower than the incident radiation, representing the photons that suffered loss of energy due to inelastic (Compton) scattering in the sample [1]. The number of photons Rayleigh (NR) and Compton (NC) scattered from the material at a scattering angle y detected by the detector are related to the areas of their respective peaks in the measured spectrum and can be written by the following equations, respectively: Fig. 1. Experimental arrangement.
Table 1 Chemical formula and mass density of reference materials used for validation of the method. Reference material
Chemical formula
r (g/cm3)
Water Ethanol Isopropanol Glycerol Dimethylformamide Acrylic Nylon
H2O C2H6O C3H8O C3H8O3 C3H7NO (C6H8O2)n (C6H11NO)n
1.00 0.79 0.78 1.26 0.95 1.19 1.15
A zirconium filter (Zr, Z¼40) was used to filter out the Mo Kb line. Then, a graphite monochromator was used in order to select the fluorescence line (Ka). The beam size was limited by two slits S1 (0.5 0.5 mm2) and S2 (0.75 0.75 mm2), placed in the entrance and exit of the monochromator, respectively. The flux rate on the sample was of the order of 106 photons/s cm2. An additional set of circular (f ¼2 mm) slits, S3 and S4, separated by 15 mm, was placed in front of the detector. The experimental geometry was in reflection mode with a scattering angle (y) of 901, corresponding to a momentum transfer value of x¼0.99 A˚ 1. The detection system consisted of a Si(Li) detector (Canberra SL30165) with energy resolution of 165 eV at 5.9 keV, coupled to a multichannel analyzer (MCA), which allows discriminating the peaks of elastic and inelastic scatterings. The time for each measurement was 1000 s, in order to reduce the statistical uncertainties in the counts, both for the elastic and inelastic peaks, to less than 1%. 2.2. Samples The breast tissue samples were obtained from surgical procedures of mastectomy (surgical removal of a breast to remove a malignant tumor) or from procedures of mastoplasty (plastic surgery for breast reduction). A total of 109 samples of breast tissues was analyzed, 65 of them histologically classified as normal (49 adipose and 16 fibroglandular), 10 as benign (fibroadenomas) and 34 as malignant (carcinomas) breast tissues. The sample thickness (6 mm) was chosen in order to provide sufficient single scattering events while minimizing the probability of multiple scattering [30]. Several reference materials (water, ethanol, isopropanol, glycerol, dimethylformamide, acrylic and nylon) were used to validate the method. They were chosen due to their similar elemental composition with breast tissues [20,22]. Their chemical formula and mass physical density are shown in Table 1.
NR ¼ N0 nat ½ðds=dOÞTh F 2 ðx,ZÞDOV eAR
ð1Þ
NC ¼ N0 nat ½ðds=dOÞKN Sðx,ZÞDOV eAC
ð2Þ
where N0 is the number of incident photons per unit area, nat the number of atoms per volume of sample material (nat ¼NAr/A, where NA is Avogadro’s number, r is the physical density and A is the atomic mass), (ds/dO)Th and (ds/dO)KN correspond to the Thomson and Klein–Nishina differential cross-sections, respectively, F is the atomic form factor [31,32] and S the incoherent scattering function [31], which are both dependent on the momentum transfer (x), 1 defined as x ¼ l sinðy=2Þ, where l is the wavelength of the incident photon, and the atomic number Z; DO is the solid angle subtended by the detector, V is the scatterer volume, e is the detector efficiency R R and AR ¼ 1=V V e½mðE0 ÞLi þ mðE0 ÞLS dV and AC ¼ 1=V V e½mðE0 ÞLi þ mðEC ÞLS dV are the self-attenuation factors for the Rayleigh and Compton scattering, respectively, where m(E0) and m(EC) are the linear attenuation coefficient for the incident (E0) and Compton (EC) scattered energy, respectively, Li is the distance from surface of the sample to the elemental scattering volume (dV) and LS from this element to the surface of the sample, in the direction of the detector. The Rayleigh to Compton scattering ratio ðRÞ can then be written as ðds=dOÞTh F 2 ðx,ZÞ AR NR Rðx,ZÞ ¼ ¼ ð3Þ NC ðds=dOÞKN Sðx,ZÞ AC In order to obtain the Rayleigh to Compton scattering ratio ðRÞ independent of the attenuation in the sample we must choose an experimental condition (E0,y) in which the shift in energy between the Rayleigh and Compton scattering must be small (EC EE0) to give the ratio AR =AC 1, but sufficient to allow a good separation between the Rayleigh and Compton components in the measured spectrum [23]. Thus, we can write 2 ððds=dOÞÞTh F ðx,ZÞ Rðx,ZÞ ¼ ð4Þ Sðx,ZÞ ðds=dOÞKN For compounds and mixtures containing various elements (such as tissues or reference materials) we can generalize Eq. (4) using the independent atomic model (IAM), which assumes that each atom scatters independently of the other, so that no interference effects are produced # "P at 2 a F ðx,Zi Þ ðds=dOÞTh Rðx,Zeff Þ ¼ Pi i at ð5Þ ðds=dOÞKN i ai Sðx,Zi Þ where the atomic fraction aat i can be obtained in terms of mass fraction oi and the atomic mass Ai of the ith element
oi =Ai aat i ¼ P i oi =Ai
ð6Þ
M. Antoniassi et al. / Nuclear Instruments and Methods in Physics Research A 652 (2011) 739–743
In this way, for a given experimental momentum transfer x, we have that the ratio R is a function of effective atomic number (Zeff), which is a complicated function of the atomic numbers of the elements present in the mixture [23,33]: R ¼ fx ðZeff Þ. The function R ¼ fx ðZeff Þ can be obtained fitting, with an adequate mathematical function, the points of the discrete function R ¼ fx ðZÞ for the pure chemical elements, constructed with theoretical R values (calculated using equation 4). The continuous line in Fig. 2 shows the functionR ¼ f0:99 ðZeff Þ, obtained by a six-order polynomial fitting of theoretical values of R (symbols), for chemical elements of atomic number Z ¼1 to 12, using the values of F(x,Z) of Schaupp et al. [32] and S(x, Z) of Hubbell et al. [31] where the value of x¼0.99 A˚ 1 corresponds to the experimental momentum transfer. This obtained function allows determining the values of effective atomic number of a particular material or tissue using the ratio between the number of Rayleigh (NR) and Compton (NC) scattering photons obtained from experimental measurements. The number of Rayleigh (NR) and Compton (NC) scattered photons was obtained by determining the area under the curve of each scattering peak in the measured spectrum. Since there is overlap between the curves of Rayleigh and Compton scattering, a Gaussian curve fitting procedure was used for determining the areas of each peak. The R2 values obtained were always better than 0.98. The validity of the method was tested comparing the values of Zeff of different standard compounds determined using the experimental Rayleigh to Compton ratios (proposed method) and Zeff values for photon interaction obtained experimentally
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using the conventional method based on the total cross-section of the compounds. This last method involves finding by interpolation the effective atomic number that corresponds to the total cross-section of the compound material on a plot of total crosssection for the pure elements versus atomic number [24]. The total cross-sections are obtained dividing the mass attenuation coefficient m/r by the number of atoms present in one gram of compound material. In this work the m/r values of the reference materials were obtained from the experimental linear attenuation coefficients (m) determined through transmission measurements aligning the detector with the incident beam (y ¼01) and using the physical densities present in Table 1.
3. Results and discussions 3.1. Validation of the method Table 2 compares the effective atomic number of the reference materials determined by the method proposed in this work, which uses the measured Rayleigh and Compton scattering ratio (scattering method), and by the conventional method, based on the total cross-sections [24] (transmission method). The experimental uncertainties represent the statistical uncertainties in the obtained Zeff values, which are a combination of statistical uncertainties associated with the counts and experimental procedure. From the table, a good agreement between both methods (differences up to 5%) is observed, showing that the proposed scattering method can be used, with the advantage of being less sensitive to sample variation of thickness and positioning (particularly a problem in transmission measurements, when using biological tissues), giving lesser experimental uncertainties. 3.2. Effective atomic number of the tissues
Fig. 2. Rayleigh to Compton ratio R as a function of the effective atomic number Zeff. Symbols represent the theoretical R values calculated using Eq. (4), for the pure chemical elements. The continuous line is the result of a six-order polynomial fit.
In Fig. 3 a box and whisker plot are shown for our data. From this figure is possible to observe that the effective atomic number distributions of the breast tissues are broad. These variations are expected and can be attributed either to general parameters (associated to the sampling of different patients) such as diet, medication, environment, age, hormonal status, genetics, or to specific parameters associated to particular histological characteristic of the tissue type, which explain the large variation of the distributions of the fibroglandular tissues (composed of a variable amount of lipids between the fibers) and of carcinomas (composed of a variable amount of fibers and malignant epithelium cells [34]). On the other hand, the fibroadenomas showed the smallest variation, fact related to the spatial regularity and homogeneity of their histological constituents [34]. Fig. 3 also shows that adipose breast tissues present smaller effective atomic number values than normal fibroglandular and neoplastic (benign and malignant) tissues. It was expected
Table 2 Zeff of reference materials determined by the proposed method (scattering method) and by the conventional method (transmission method). Reference material
Zeff (scattering method)
Zeff (transmission method)
Difference (%)
Water Ethanol Isopropanol Glycerol Dimethylformamaide Acrylic Nylon
5.85 7 0.05 5.26 7 0.06 5.21 7 0.05 5.64 7 0.04 5.36 7 0.05 5.53 7 0.05 5.34 7 0.07
5.907 0.09 5.037 0.12 4.967 0.08 5.657 0.07 5.247 0.09 5.487 0.11 5.097 0.11
0.9 4.4 4.8 0.2 2.2 0.9 4.7
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because the adipose tissue is composed mainly of specialized cells in storage lipids, called adipocytes, rich in carbon (Z¼6) [35], while fibroglandular and neoplastic breast tissues are of conjunctive or epithelial origin (rich in fiber of collagen and water), presenting a higher oxygen composition (Z¼8) [5,8] then a more elevated effective atomic number. The differences of carbon and oxygen composition of breast tissues can be observed in Table 3, which compares the mass percentage of carbon and oxygen obtained by Hammerstein et al. [36] Poletti et al. [5,8] and Woodard and White [35]. There has been no composition values published for fibroadenoma but it is possible to conclude from Fig. 3 that its composition is similar to those for fibroglandular or carcinomas tissues. The mean (M) values of effective atomic number of each tissue type, and the intervals M + s and M s obtained are shown in Table 4. The mean values found are in very good agreement with theoretical calculated values of effective atomic number for photon interaction (15 keV) of adipose (Zeff ¼5.2358) and fibroglandular breast tissue (Zeff ¼ 5.7539) reported by Shivaramu [24], whose values are, respectively, 2.6% and 0.9% smaller than the values found in this study. Experimental values of mean atomic
P number, defined as Z mean ¼ i oi Zi , reported by Ryan and Farquharson [29], although not the same physical quantity obtained in this study, can be used as a qualitative source of comparison. Their results, in agreement with the results of this work, show that the malignant tissues values were found to be higher than normal fibroglandular tissues. No comparison was made with fibroadenomas (benign neoplasias) since there is no published data related to atomic number of this tissue type in literature. However, the results obtained in this study found a difference in effective atomic number of fibroadenoma and adipose tissue of 8.4%. Finally, statistical comparisons were carried out in the distributions set, in order to quantify the potential use of effective atomic number to differentiate samples according to their histological classifications. The conditions of normality and homoscedasticity of distributions for application of parametric tests were confirmed by Kolmogorov–Smirnov and Bartlett test, respectively. The statistical comparisons took the form of a one-way analysis of variance (ANOVA) with the Bonferroni test applied as a post-hoc test, showing significant differences between the normal adipose tissue and all other investigated tissue type (p-valueo0.01) and between fibroglandular and fibroadenoma (p-valueo0.1).
4. Conclusions This work presented a procedure to determine effective atomic number of normal and neoplastic breast tissues through measurements of elastic and inelastic scattering intensity using a photon energy of 17.44 keV (Ka radiation of Mo). The experimental method generates uncertainties estimated less than 3%. The results showed that adipose breast tissue has smaller effective atomic number than fibroglandular and neoplastic breast tissues (fibroadenoma and carcinoma), fact related to the carbon and oxygen composition of these tissues. The effective atomic number values obtained in this work are in good agreement with previous theoretical and experimental published data. Finally, the statistical analysis showed differences between groups of tissues, pointing the possibility of using the technique to characterize and differentiate the tissues types. Therefore, it is expected that the data on effective atomic number presented here will be useful in view of their importance in the field of medical imaging and dosimetry. In the next stage of the analysis, the
Fig. 3. Box plot of the effective atomic number results for each tissue type.
Table 3 Chemical composition (weight percentage) of carbon and oxygen of breast tissues in literature. Chemical element
Adipose Fibroglandular Carcinoma a b
Hammerstein et al. [36]
Poletti et al. [5,8]
Woodard and White [35]
C (Z ¼6) (wt%)
O (Z¼ 8) (wt%)
C (Z¼ 6) (wt%)
O (Z ¼8) (wt%)
C (Z ¼6) (wt%)
O (Z¼ 8) (wt%)
61.9 18.4 NM
25.1 67.7 NM
76.5 7 1.1a 18.4 7 0.9a 20.36b
10.77 1.3a 67.9 7 2.0a 65.98b
59.8 33.2 NM
27.8 52.7 NM
Weight percentage presented by Poletti et al. [8]. Mean percentage of carcinomas presented by Poletti et al. [5].
Table 4 Range of determined mean values of effective atomic number of breast tissues.
Ms Mean, M M+s
Adipose (Zeff)
Fibroglandular (Zeff)
Fibroadenoma (Zeff)
Carcinoma (Zeff)
5.368 5.375 5.382
5.796 5.806 5.816
5.866 5.862 5.858
5.836 5.843 5.850
M. Antoniassi et al. / Nuclear Instruments and Methods in Physics Research A 652 (2011) 739–743
sensibility of the method at different momentum transfer values will be studied for future improvement of this work.
Acknowledgments The authors would like to acknowledge the support by the Brazilian agencies Fundac- a~ o de Amparo a Pesquisa do Estado de Sa~ o Paulo (FAPESP) and Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico (CNPq). We also would like to thank the Department of Pathology of the Clinics Hospital, Faculty of Medicine of Ribeira~ o Preto, Brazil, for allowing collection of the human breast samples. References [1] [2] [3] [4] [5] [6] [7]
[8] [9]
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[12] K.K.W. Siu, S.M. Butler, T. Beveridge, J.E. Gillam, C.J. Hall, A.H. Kaye, R.A. Lewis, ¨ K. Mannan, G. McLoughlin, S. Pearson, A.R. Round, E. Schultke, G.I. Webb, S.J. Wilkinson, Nucl. Instr. and Meth. A 548 (2005) 140. [13] C.R.F. Castro, R.C. Barroso, R.T. Lopes, X-ray Spectrom. 34 (2005) 477. [14] W.M. Elshemey, A.A. Elsayed, A. El-Lakkani, Phys. Med. Biol. 44 (1999) 2907. [15] J.M. Sharaf, Appl. Radiat. Isot. 54 (2001) 801. [16] R.L. Clarke, G. Van Dyk, Phys. Med. Biol. 18 (1973) 532. [17] A.L. Huddleston, D. Bhaduri, Phys. Med. Biol. 24 (1979) 310. [18] C.E. Webber, G. Coates, Med. Phys. 9 (1982) 473. [19] J.A. Hanson, W.E. Moore, M.M. Figley, P.R. Duke, Med. Phys. 11 (1984) 633. [20] J.S. Al-Bahri, N.M. Spyrou, Appl. Radiat. Isot. 49 (1998) 1677. [21] E.A. Ryan, M.J. Farquharson, D.M. Flinton, Phys. Med. Biol. 50 (2005) 3337. [22] M. Antoniassi, A.L.C Conceic- a~ o, M.E. Poletti, Nucl. Instr. and Meth. A 619 (2010) 375. [23] P. Duvauchelle, G. Peix, D. Babot, Nucl. Instr. and Meth. B 155 (1999) 221. [24] Shivaramu, Med. Dosim. 27 (2002) 1. [25] P. Puumalainen, P. Sikanen, H. Olkkonen, Nucl. Instr. and Meth. 163 (1979) 261. [26] P. Puumalainen, H. Olkkonen, P. Sikanen, Int. J. Appl. Radiat. Isot. 28 (1977) 785. [27] S.A. Kerr, K. Kouris, C.E. Webber, T.J. Kennett, Phys. Med. Biol. 25 (1980) 1037. [28] P. Puumalainen, A. Uimarihuhta, H. Olkkonen, E.M. Alhava, Phys. Med. Biol. 27 (1982) 425. [29] E.A. Ryan, M.J. Farquharson, Nucl. Instr. and Meth. A 619 (2010) 379. [30] P.P. Kane, L. Kissel, R.H. Pratt, S.C. Roy, Phys. Rep. 140 (1986) 75. [31] J.H. Hubbell, W.J. Veigele, E.A. Briggs, R.T. Brown, D.T. Cromer, R.J. Howerton, J. Phys. Chem. Ref. Data 4 (1975) 471; J.H. Hubbell, W.J. Veigele, E.A. Briggs, R.T. Brown, D.T. Cromer, R.J. Howerton, Erratum 6 (1977) 615. [32] D. Schaupp, M. Schumacher, F. Smend, P. Rullhusen, J.H. Hubbell, J. Phys. Chem. Ref. Data 12 (1983) 467. [33] D.A. Bradley, A.M. Ghose, Phys. Med. Biol. 29 (1984) 1385. [34] P.P Rosen, in: Rosen’s Breast Pathology, 3rd ed., Lippincott Williams & Wilkins, Philadelphia, 2009. [35] H.Q Woodard, D.R. White., Br. J. Radiol. 59 (1986) 1209. [36] G.R. Hammerstein, D.W. Miller, R. White, M.E. Masterson, H.Q. Woodard, J.S. Laughlin, Radiol 130 (1979) 485.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Study of effective atomic number of breast tissues determined using the elastic to inelastic scattering ratio M. Antoniassi, A.L.C. Conceic- a~ o, M.E. Poletti n ~ Preto, Universidade de Sa~ o Paulo, Ribeirao ~ Preto, Sa~ o Paulo, Brazil ´tica, Faculdade de Filosofia Ciˆencias e Letras de Ribeirao Departamento de Fı´sica e Matema
a r t i c l e in fo
abstract
Available online 1 October 2010
In this work we have measured Compton and Rayleigh scattering radiation from normal (adipose and fibroglandular), benign (fibroadenoma) and malignant (ductal carcinoma) breast tissues using a monoenergetic beam of 17.44 keV and a scattering angle of 901 (x ¼ 0.99 A˚ 1). A practical method using the area of Rayleigh and Compton scattering was used for determining the effective atomic number (Zeff) of the samples, being validated through measurements of several reference materials. The results show that there are differences in the distributions of Zeff of breast tissues, which are mainly related to the elemental composition of carbon (Z ¼6) and oxygen (Z¼ 8) of each tissue type. The results suggest that is possible to use the method to characterize the breast tissues permitting study histological features of the breast tissues related to their elemental composition. & 2010 Elsevier B.V. All rights reserved.
Keywords: Effective atomic number Elastic scattering Inelastic scattering Breast cancer
1. Introduction The scattered radiation both elastically (Rayleigh) and inelastically (Compton) has been widely reported as an important tool for characterization of materials [1–3]. Specifically for medical purposes, it has been successfully used to characterize biological tissues [4–6]. The elastic scattering allows obtaining the spatial distribution of the scattering centers (atoms or molecules) giving detailed information about the chemical structures of the tissues, being applied for different tissues like breast [7–11], brain [12], kidney [13], uterus [13] and muscle [14]. On the other hand, the inelastic (Compton) scattering allows assessing the electron density of the tissues [15], since its intensity depends upon the number of scattering centers (electrons) in sample volume, being applied successfully in bone [16,17], lung [18,19] and breast densitometry [20–22] for osteoporosis, lung oedema and breast cancer diagnoses, respectively. The combination of elastic and inelastic scattering through the ratio of their intensities, will give a quantity dependent only on a function of the atomic number [23], independent of the density and attenuation inside the sample, which allows determining the effective atomic number of the human tissues, an important quantity used in medical imaging (particularly in tomographic systems) and dosimetry [24]. When compared with conventional transmission techniques, sensitive to linear attenuation coefficient (m), this technique is especially useful in cases where variations
n
Corresponding author. Tel.: + 55 16 3602 4442; fax: + 55 16 3602 4887. E-mail address: [email protected] (M.E. Poletti).
0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.09.110
of m are small, and the atomic number variations become more significant. It has been used to detect changes in the composition of soft tissue [25], liver [26] and trabecular bone [27,28]. However, there are few works for breast tissue characterization [29]. For this purpose, Ryan and Farquharson [29] measured elastic and inelastic scattering of normal (healthy) and malignant breast tissues using a monoenergetic synchrotron beam of 10 keV and a scattering angle of 1201. Gelatine-based gel mixtures were used to calibrate the system in order to obtain the mean atomic number of the tissues from the elastic to inelastic scattering ratio. In the present work we have measured elastic and inelastic scattering radiation from normal (adipose and fibroglandular), benign (fibroadenoma) and malignant (carcinoma) breast tissues using a monoenergetic beam of 17.44 keV and a scattering angle of 901 (x ¼0.99 A˚ 1). A practical method using the area of elastic and inelastic scattering was used for determining the effective atomic number (Zeff) [23] of the breast tissues. This work also discusses the results on the basis of histological characteristics and elemental composition of the tissues. Finally, statistical comparisons were made in order to evaluate the potential use of effective atomic number to classify breast tissues.
2. Materials and method 2.1. Experimental arrangement The experimental set-up is shown in Fig. 1. The X-ray tube used was a Mo (Z¼42, Ka ¼17.44 keV, Kb ¼ 19.6 keV) coupled to a high voltage generator of 4 kV operating at 35 kVp and 45 mA.
740
M. Antoniassi et al. / Nuclear Instruments and Methods in Physics Research A 652 (2011) 739–743
2.3. Method When a detector is placed in a determined angle relative to the incident direction of the radiation (scattering angle), usually two features are detected (considering a high energy resolution detection system): a narrow peak in the same energy of the incident radiation, corresponding to the photons elastically (Rayleigh) scattered and a wide peak with energy lower than the incident radiation, representing the photons that suffered loss of energy due to inelastic (Compton) scattering in the sample [1]. The number of photons Rayleigh (NR) and Compton (NC) scattered from the material at a scattering angle y detected by the detector are related to the areas of their respective peaks in the measured spectrum and can be written by the following equations, respectively: Fig. 1. Experimental arrangement.
Table 1 Chemical formula and mass density of reference materials used for validation of the method. Reference material
Chemical formula
r (g/cm3)
Water Ethanol Isopropanol Glycerol Dimethylformamide Acrylic Nylon
H2O C2H6O C3H8O C3H8O3 C3H7NO (C6H8O2)n (C6H11NO)n
1.00 0.79 0.78 1.26 0.95 1.19 1.15
A zirconium filter (Zr, Z¼40) was used to filter out the Mo Kb line. Then, a graphite monochromator was used in order to select the fluorescence line (Ka). The beam size was limited by two slits S1 (0.5 0.5 mm2) and S2 (0.75 0.75 mm2), placed in the entrance and exit of the monochromator, respectively. The flux rate on the sample was of the order of 106 photons/s cm2. An additional set of circular (f ¼2 mm) slits, S3 and S4, separated by 15 mm, was placed in front of the detector. The experimental geometry was in reflection mode with a scattering angle (y) of 901, corresponding to a momentum transfer value of x¼0.99 A˚ 1. The detection system consisted of a Si(Li) detector (Canberra SL30165) with energy resolution of 165 eV at 5.9 keV, coupled to a multichannel analyzer (MCA), which allows discriminating the peaks of elastic and inelastic scatterings. The time for each measurement was 1000 s, in order to reduce the statistical uncertainties in the counts, both for the elastic and inelastic peaks, to less than 1%. 2.2. Samples The breast tissue samples were obtained from surgical procedures of mastectomy (surgical removal of a breast to remove a malignant tumor) or from procedures of mastoplasty (plastic surgery for breast reduction). A total of 109 samples of breast tissues was analyzed, 65 of them histologically classified as normal (49 adipose and 16 fibroglandular), 10 as benign (fibroadenomas) and 34 as malignant (carcinomas) breast tissues. The sample thickness (6 mm) was chosen in order to provide sufficient single scattering events while minimizing the probability of multiple scattering [30]. Several reference materials (water, ethanol, isopropanol, glycerol, dimethylformamide, acrylic and nylon) were used to validate the method. They were chosen due to their similar elemental composition with breast tissues [20,22]. Their chemical formula and mass physical density are shown in Table 1.
NR ¼ N0 nat ½ðds=dOÞTh F 2 ðx,ZÞDOV eAR
ð1Þ
NC ¼ N0 nat ½ðds=dOÞKN Sðx,ZÞDOV eAC
ð2Þ
where N0 is the number of incident photons per unit area, nat the number of atoms per volume of sample material (nat ¼NAr/A, where NA is Avogadro’s number, r is the physical density and A is the atomic mass), (ds/dO)Th and (ds/dO)KN correspond to the Thomson and Klein–Nishina differential cross-sections, respectively, F is the atomic form factor [31,32] and S the incoherent scattering function [31], which are both dependent on the momentum transfer (x), 1 defined as x ¼ l sinðy=2Þ, where l is the wavelength of the incident photon, and the atomic number Z; DO is the solid angle subtended by the detector, V is the scatterer volume, e is the detector efficiency R R and AR ¼ 1=V V e½mðE0 ÞLi þ mðE0 ÞLS dV and AC ¼ 1=V V e½mðE0 ÞLi þ mðEC ÞLS dV are the self-attenuation factors for the Rayleigh and Compton scattering, respectively, where m(E0) and m(EC) are the linear attenuation coefficient for the incident (E0) and Compton (EC) scattered energy, respectively, Li is the distance from surface of the sample to the elemental scattering volume (dV) and LS from this element to the surface of the sample, in the direction of the detector. The Rayleigh to Compton scattering ratio ðRÞ can then be written as ðds=dOÞTh F 2 ðx,ZÞ AR NR Rðx,ZÞ ¼ ¼ ð3Þ NC ðds=dOÞKN Sðx,ZÞ AC In order to obtain the Rayleigh to Compton scattering ratio ðRÞ independent of the attenuation in the sample we must choose an experimental condition (E0,y) in which the shift in energy between the Rayleigh and Compton scattering must be small (EC EE0) to give the ratio AR =AC 1, but sufficient to allow a good separation between the Rayleigh and Compton components in the measured spectrum [23]. Thus, we can write 2 ððds=dOÞÞTh F ðx,ZÞ Rðx,ZÞ ¼ ð4Þ Sðx,ZÞ ðds=dOÞKN For compounds and mixtures containing various elements (such as tissues or reference materials) we can generalize Eq. (4) using the independent atomic model (IAM), which assumes that each atom scatters independently of the other, so that no interference effects are produced # "P at 2 a F ðx,Zi Þ ðds=dOÞTh Rðx,Zeff Þ ¼ Pi i at ð5Þ ðds=dOÞKN i ai Sðx,Zi Þ where the atomic fraction aat i can be obtained in terms of mass fraction oi and the atomic mass Ai of the ith element
oi =Ai aat i ¼ P i oi =Ai
ð6Þ
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In this way, for a given experimental momentum transfer x, we have that the ratio R is a function of effective atomic number (Zeff), which is a complicated function of the atomic numbers of the elements present in the mixture [23,33]: R ¼ fx ðZeff Þ. The function R ¼ fx ðZeff Þ can be obtained fitting, with an adequate mathematical function, the points of the discrete function R ¼ fx ðZÞ for the pure chemical elements, constructed with theoretical R values (calculated using equation 4). The continuous line in Fig. 2 shows the functionR ¼ f0:99 ðZeff Þ, obtained by a six-order polynomial fitting of theoretical values of R (symbols), for chemical elements of atomic number Z ¼1 to 12, using the values of F(x,Z) of Schaupp et al. [32] and S(x, Z) of Hubbell et al. [31] where the value of x¼0.99 A˚ 1 corresponds to the experimental momentum transfer. This obtained function allows determining the values of effective atomic number of a particular material or tissue using the ratio between the number of Rayleigh (NR) and Compton (NC) scattering photons obtained from experimental measurements. The number of Rayleigh (NR) and Compton (NC) scattered photons was obtained by determining the area under the curve of each scattering peak in the measured spectrum. Since there is overlap between the curves of Rayleigh and Compton scattering, a Gaussian curve fitting procedure was used for determining the areas of each peak. The R2 values obtained were always better than 0.98. The validity of the method was tested comparing the values of Zeff of different standard compounds determined using the experimental Rayleigh to Compton ratios (proposed method) and Zeff values for photon interaction obtained experimentally
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using the conventional method based on the total cross-section of the compounds. This last method involves finding by interpolation the effective atomic number that corresponds to the total cross-section of the compound material on a plot of total crosssection for the pure elements versus atomic number [24]. The total cross-sections are obtained dividing the mass attenuation coefficient m/r by the number of atoms present in one gram of compound material. In this work the m/r values of the reference materials were obtained from the experimental linear attenuation coefficients (m) determined through transmission measurements aligning the detector with the incident beam (y ¼01) and using the physical densities present in Table 1.
3. Results and discussions 3.1. Validation of the method Table 2 compares the effective atomic number of the reference materials determined by the method proposed in this work, which uses the measured Rayleigh and Compton scattering ratio (scattering method), and by the conventional method, based on the total cross-sections [24] (transmission method). The experimental uncertainties represent the statistical uncertainties in the obtained Zeff values, which are a combination of statistical uncertainties associated with the counts and experimental procedure. From the table, a good agreement between both methods (differences up to 5%) is observed, showing that the proposed scattering method can be used, with the advantage of being less sensitive to sample variation of thickness and positioning (particularly a problem in transmission measurements, when using biological tissues), giving lesser experimental uncertainties. 3.2. Effective atomic number of the tissues
Fig. 2. Rayleigh to Compton ratio R as a function of the effective atomic number Zeff. Symbols represent the theoretical R values calculated using Eq. (4), for the pure chemical elements. The continuous line is the result of a six-order polynomial fit.
In Fig. 3 a box and whisker plot are shown for our data. From this figure is possible to observe that the effective atomic number distributions of the breast tissues are broad. These variations are expected and can be attributed either to general parameters (associated to the sampling of different patients) such as diet, medication, environment, age, hormonal status, genetics, or to specific parameters associated to particular histological characteristic of the tissue type, which explain the large variation of the distributions of the fibroglandular tissues (composed of a variable amount of lipids between the fibers) and of carcinomas (composed of a variable amount of fibers and malignant epithelium cells [34]). On the other hand, the fibroadenomas showed the smallest variation, fact related to the spatial regularity and homogeneity of their histological constituents [34]. Fig. 3 also shows that adipose breast tissues present smaller effective atomic number values than normal fibroglandular and neoplastic (benign and malignant) tissues. It was expected
Table 2 Zeff of reference materials determined by the proposed method (scattering method) and by the conventional method (transmission method). Reference material
Zeff (scattering method)
Zeff (transmission method)
Difference (%)
Water Ethanol Isopropanol Glycerol Dimethylformamaide Acrylic Nylon
5.85 7 0.05 5.26 7 0.06 5.21 7 0.05 5.64 7 0.04 5.36 7 0.05 5.53 7 0.05 5.34 7 0.07
5.907 0.09 5.037 0.12 4.967 0.08 5.657 0.07 5.247 0.09 5.487 0.11 5.097 0.11
0.9 4.4 4.8 0.2 2.2 0.9 4.7
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because the adipose tissue is composed mainly of specialized cells in storage lipids, called adipocytes, rich in carbon (Z¼6) [35], while fibroglandular and neoplastic breast tissues are of conjunctive or epithelial origin (rich in fiber of collagen and water), presenting a higher oxygen composition (Z¼8) [5,8] then a more elevated effective atomic number. The differences of carbon and oxygen composition of breast tissues can be observed in Table 3, which compares the mass percentage of carbon and oxygen obtained by Hammerstein et al. [36] Poletti et al. [5,8] and Woodard and White [35]. There has been no composition values published for fibroadenoma but it is possible to conclude from Fig. 3 that its composition is similar to those for fibroglandular or carcinomas tissues. The mean (M) values of effective atomic number of each tissue type, and the intervals M + s and M s obtained are shown in Table 4. The mean values found are in very good agreement with theoretical calculated values of effective atomic number for photon interaction (15 keV) of adipose (Zeff ¼5.2358) and fibroglandular breast tissue (Zeff ¼ 5.7539) reported by Shivaramu [24], whose values are, respectively, 2.6% and 0.9% smaller than the values found in this study. Experimental values of mean atomic
P number, defined as Z mean ¼ i oi Zi , reported by Ryan and Farquharson [29], although not the same physical quantity obtained in this study, can be used as a qualitative source of comparison. Their results, in agreement with the results of this work, show that the malignant tissues values were found to be higher than normal fibroglandular tissues. No comparison was made with fibroadenomas (benign neoplasias) since there is no published data related to atomic number of this tissue type in literature. However, the results obtained in this study found a difference in effective atomic number of fibroadenoma and adipose tissue of 8.4%. Finally, statistical comparisons were carried out in the distributions set, in order to quantify the potential use of effective atomic number to differentiate samples according to their histological classifications. The conditions of normality and homoscedasticity of distributions for application of parametric tests were confirmed by Kolmogorov–Smirnov and Bartlett test, respectively. The statistical comparisons took the form of a one-way analysis of variance (ANOVA) with the Bonferroni test applied as a post-hoc test, showing significant differences between the normal adipose tissue and all other investigated tissue type (p-valueo0.01) and between fibroglandular and fibroadenoma (p-valueo0.1).
4. Conclusions This work presented a procedure to determine effective atomic number of normal and neoplastic breast tissues through measurements of elastic and inelastic scattering intensity using a photon energy of 17.44 keV (Ka radiation of Mo). The experimental method generates uncertainties estimated less than 3%. The results showed that adipose breast tissue has smaller effective atomic number than fibroglandular and neoplastic breast tissues (fibroadenoma and carcinoma), fact related to the carbon and oxygen composition of these tissues. The effective atomic number values obtained in this work are in good agreement with previous theoretical and experimental published data. Finally, the statistical analysis showed differences between groups of tissues, pointing the possibility of using the technique to characterize and differentiate the tissues types. Therefore, it is expected that the data on effective atomic number presented here will be useful in view of their importance in the field of medical imaging and dosimetry. In the next stage of the analysis, the
Fig. 3. Box plot of the effective atomic number results for each tissue type.
Table 3 Chemical composition (weight percentage) of carbon and oxygen of breast tissues in literature. Chemical element
Adipose Fibroglandular Carcinoma a b
Hammerstein et al. [36]
Poletti et al. [5,8]
Woodard and White [35]
C (Z ¼6) (wt%)
O (Z¼ 8) (wt%)
C (Z¼ 6) (wt%)
O (Z ¼8) (wt%)
C (Z ¼6) (wt%)
O (Z¼ 8) (wt%)
61.9 18.4 NM
25.1 67.7 NM
76.5 7 1.1a 18.4 7 0.9a 20.36b
10.77 1.3a 67.9 7 2.0a 65.98b
59.8 33.2 NM
27.8 52.7 NM
Weight percentage presented by Poletti et al. [8]. Mean percentage of carcinomas presented by Poletti et al. [5].
Table 4 Range of determined mean values of effective atomic number of breast tissues.
Ms Mean, M M+s
Adipose (Zeff)
Fibroglandular (Zeff)
Fibroadenoma (Zeff)
Carcinoma (Zeff)
5.368 5.375 5.382
5.796 5.806 5.816
5.866 5.862 5.858
5.836 5.843 5.850
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sensibility of the method at different momentum transfer values will be studied for future improvement of this work.
Acknowledgments The authors would like to acknowledge the support by the Brazilian agencies Fundac- a~ o de Amparo a Pesquisa do Estado de Sa~ o Paulo (FAPESP) and Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico (CNPq). We also would like to thank the Department of Pathology of the Clinics Hospital, Faculty of Medicine of Ribeira~ o Preto, Brazil, for allowing collection of the human breast samples. References [1] [2] [3] [4] [5] [6] [7]
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